Map the following scenario to a graph theory problem. Explain what the vertices and the edges of the graph are and why the two problems are equivalent. Clearly mention any assumptions that you make.

You have been given the task of preparing a question paper in graph theory with 100 questions. The questions can come from 10 different categories, 10 for each category. To assist you, there , is a question bank of five hundred questions, but each question has several categories attached to it. Formulate a graph theory problem to check whether it is possible to get all the questions you want from the question bank